Would this neural network have short term memory?
Congrats, you have invented 1d convolution. Convolution combined with RNN would have some advantage over just RNN. Think about the perception field. 
In this layer, you do aggregate $6$ values to one. Imagine two of them - it will be $36$ already, etc. But, in the end, you still need RNN at the end to aggregate a variable length to constant length.